Linear integral equation

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An integral equation in which the unknown function $\phi(s)$ occurs in a linear fashion:

$$A(x)\phi(x)+\int\limits_DK(x,s)\phi(s)ds=f(x),\quad x\in D.$$

Here $A$, $K$, $f$ are given functions, $D$ is a domain of the Euclidean space, $k$ and $s$ are points of the space, and $ds$ is the volume element. For more details see Integral equation.

How to Cite This Entry:
Linear integral equation. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article